In quantum communication, two parties exchange information encoded in quantum states. Typically, the quantum states are specially defined properties of photons such as pairs of polarization states (e.g., 0° and 90°, or 45° and 135°) or circular basis states (e.g., left-handedness and right-handedness). Through the quantum communication (“QC”), the two parties produce a shared random series of bits known only to them, which can then be used as secret keys in subsequent encryption and decryption of messages. The process of producing such keys through QC is also called quantum key distribution (“QKD”).
A third party can, in theory, eavesdrop on the QC between the two parties. Such eavesdropping perturbs the QC, however, introducing anomalies that the two intended parties can detect. Using conventional communication, the two parties post-process the results of the QC to remove any partial information acquired by an eavesdropper, and form shared secret keys from the remaining information resulting from the QC.
For example, according to one general approach to QKD, a transmitter sets the quantum state of binary information, makes a record of how it set the quantum state, and transmits the information. Table 1 shows an example of quantum states and bases for different polarizations of photons. For the bases and states shown in Table 1, the transmitter selects a basis (rectilinear or diagonal), sets the polarization state for a photon in the selected basis, and records the bit value (0 or 1), the selected sending basis and the time of transmission.
TABLE 1Example bases and quantum states.Basis01Rectilinear (+)90°0°Diagonal (×)45°135° (or −45°)
A receiver receives the binary information, measures the quantum state of the information and makes a record of how it measured the quantum state. The measured state depends on how the receiver performs the measurement (e.g., with measuring basis of rectilinear or diagonal). The transmitter and receiver are expected to record different bit values in some instances because the transmitter and receiver at times set/measure the quantum-state-encoded information in different ways. Thus, after exchanging information in quantum states, the transmitter and receiver compare their records of how the quantum states were set and measured. For this comparison, the transmitter and receiver exchange information over a public channel. Then, the transmitter and receiver produce a shared series of bits (keys) from the encoded information for which quantum states were set and measured in the same way by the transmitter and receiver.
For the bases and states shown in Table 1, for example, the receiver selects a basis (rectilinear or diagonal), measures the polarization state in the selected basis, and records the measured bit value and measuring basis. No possible measuring basis can distinguish all four states, so the receiver essentially guesses either rectilinear or diagonal. If the measuring basis happens to match the sending basis, the receiver should measure the correct bit value. If the measuring basis does not match the sending basis, however, the measured bit value is as likely to be correct as incorrect. For example, if the sending basis is diagonal for the bit value 0 (polarization state of 45°) but the measuring basis is rectilinear, the measured bit values of 0 (90°) and 1 (0°) are equally likely. The transmitter and receiver compare the sending basis and measuring basis for a given photon, and keep the bit value for a photon if the sending basis and measuring basis match.
If an eavesdropper intercepts and measures a photon, the measurement perturbs the quantum state of the photon. The eavesdropper can only guess the original sending basis when it re-encodes and re-transmits the photon to the intended destination. At the time of measurement by the receiver, the eavesdropping is not detected. Instead, for subsets of the bit values for which sending basis and measuring basis are found to match, the transmitter and receiver compare parity values. The parity values should match exactly, if the system is appropriately tuned and free from imperfections in transmission and reception. Eavesdropping introduces noticeable discrepancies in the bit values, which allows the transmitter and receiver to detect the eavesdropping, correct the keys, and establish an upper limit on the eavesdropper's partial information.
An error-free bit string shared by the transmitter and receiver can then be privacy-amplified (e.g., by hashing with a hashing function) to reduce its length. (Or, bits can simply be dropped, but this lacks advantages of privacy amplification.) The final length of the shared bit string can depend on the number of errors detected. Shortening the shared bit string with privacy amplification reduces knowledge an eavesdropper might have to an arbitrarily low level—typically, much less than a single bit.
Other approaches to QC exploit other quantum properties (e.g., quantum entanglement) to exchange information encoded in quantum states. In addition, techniques such as privacy amplification can be used to eliminate the partial information that an eavesdropper can acquire. Techniques such as information reconciliation can be used to resolve small discrepancies in the shared bit values of the transmitter and receiver.
The theoretical framework for QC has been established for over 25 years, and its advantages in terms of security of keys are well accepted. Over the past two decades, implementations of QKD systems have become cheaper, more reliable, easier to maintain (e.g., self-tuning, self-checking), and easier to use. Previous QKD devices and technologies do not address certain practical problems of message authentication, however.
In particular, many infrastructure systems have stringent requirements in terms of information assurance (high level of security) and latency (low delay). Examples of such systems include electric grid systems, water systems, industrial control systems and high-speed financial trading systems. Typically, communications in such systems are expected to be provided with assurances of authenticity, confidentiality (e.g., for defense in depth, or to deny competitors access to information that could have trading value), non-repudiation (to prevent a sender from denying it sent a message) and freshness (to protect against replay of messages that disrupts or attacks a system). Moreover, such assurances are expected to be provided without exceeding tight latency constraints.
These security and latency requirements are challenging to satisfy using conventional non-quantum approaches to cryptography or existing QKD approaches. Conventional approaches to cryptography can provide message receivers with assurances about authenticity of the origin of multicast messages in order to protect against impersonation, substitution or replay attacks. In the context of many infrastructure systems, however, it is difficult to concurrently satisfy expectations for security and latency. For example, although appending a message authentication code tag to a message using a pre-shared group key may be sufficiently fast, it would be vulnerable to compromise of a single node. As another example, for public key cryptography, computations are too time-consuming when implemented on typical processors. Authentication with symmetric key cryptography and keyed message authentication code tags has latency problems associated with buffering of a message to determine the tag at the transmitter and hold-back of the message at the receiver to confirm the tag.